Abstract
A numerical method is proposed based on the extended cubic B-spline functions for solving the model of European call option. The Black-Scholes equation is fully-discretized by using the extended cubic B-spline collocation for spatial discretization and the finite difference method for the time discretization. The stability of difference scheme is analysed and the stability condition is given. The accuracy of this method can be improved by properly choosing the values of the parameter λ. A numerical experiment is performed to show the accuracy and stability of the proposed method.
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